Find the derivatives of the following functions at the indicated points :
Derivative of a function f(x) at any real number a is given by –
{where h is a very small positive number}
∴ derivative of sin 2x at x = π/2 is given as –
{∵ sin (π + x) = – sin x & sin π = 0}
∵ we can’t find the limit by direct substitution as it gives 0/0 (indeterminate form)
We need to use sandwich theorem to evaluate the limit.
Multiplying 2 in numerator and denominator to apply the formula.
⇒ f’(π/2) = –
Use the formula:
∴ f’(π/2) = – 2×1 = – 2
Hence,
Derivative of f(x) = sin 2x at x = π/2 is – 2